A NOTE ON THE FIRST LAYERS OF ℤp-EXTENSIONS

Title & Authors
A NOTE ON THE FIRST LAYERS OF ℤp-EXTENSIONS
Oh, Jang-Heon;

Abstract
In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic $\small{{\mathbb{Z}}_3}$-extension of an imaginary quadratic field is unramified everywhere.
Keywords
Minkowski unit;anti-cyclotomic extension;$\small{{\mathbb{Z}}_p}$-extension;
Language
English
Cited by
1.
A p-TH ROOT OF A MINKOWSKI UNIT,;

충청수학회지, 2010. vol.23. 4, pp.625-628
2.
CONSTRUCTION OF THE FIRST LAYER OF ANTI-CYCLOTOMIC EXTENSION,;

Korean Journal of Mathematics, 2013. vol.21. 3, pp.265-270
3.
ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD,;

Korean Journal of Mathematics, 2015. vol.23. 3, pp.323-326
1.
CONSTRUCTION OF THE FIRST LAYER OF ANTI-CYCLOTOMIC EXTENSION, Korean Journal of Mathematics, 2013, 21, 3, 265
2.
ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD, Korean Journal of Mathematics, 2015, 23, 3, 323
3.
ANTI-CYCLOTOMIC EXTENSION AND HILBERT CLASS FIELD, Journal of the Chungcheong Mathematical Society , 2012, 25, 1, 91
References
1.
J. Minardi, Iwasawa modules for \$Z_p^d\$-extensions of algebraic number fields, Ph. D. dissertation, University of Washington, 1986.

2.
J. Oh, Defining Polynomial of the first layer of anti-cyclotomic \$\mathbb{Z}_3\$-extension of imaginary quadratic fields of class number 1, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 3, 18-19.

3.
J. Oh, The first layer of \$\mathbb{Z}^2_2\$-extension over imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 9, 132-134.

4.
J. Oh, , On the first layer of anti-cyclotomic \$\mathbb{Z}_p\$-extension of imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 3, 19-20.

5.
L. Washington, Introduction to Cyclotomic Fields, Graduate Text in Math. Vol. 83, Springer-Verlag, 1982.